#include "rect.h"
#include "bits/stdc++.h"
#define MAXN 100009
#define INF 1000000007
#define mp(x,y) make_pair(x,y)
#define all(v) v.begin(),v.end()
#define pb(x) push_back(x)
#define wr cout<<"----------------"<<endl;
#define ppb() pop_back()
#define tr(ii,c) for(__typeof((c).begin()) ii=(c).begin();ii!=(c).end();ii++)
#define ff first
#define ss second
#define my_little_dodge 46
#define debug(x,y,z) cerr<< #x <<" = "<< x<<" "<< #y <<" = "<< y<<" "<< #z <<" = "<< z<<endl;
using namespace std;
typedef long long ll;
typedef pair<int,int> PII;
template<class T>bool umin(T& a,T b){if(a>b){a=b;return 1;}return 0;}
template<class T>bool umax(T& a,T b){if(a<b){a=b;return 1;}return 0;}
const int N=2505;
int ata[N],mn[N],mx[N],arr[N],c[N],sz,sub[N],vis[N],rc,pos;
vector<int>row[N][N],col[N][N];
vector<pair<PII,int> >addc[N];
vector<PII>remc[N];
int F[N][N];
bool cmp(int x,int y){
return (arr[x]<arr[y]);
}
int tap(int x){
if(ata[x]==x)return x;
return ata[x]=tap(ata[x]);
}
void merge(int x,int y){
if((x=tap(x))==(y=tap(y)))return;
if(sub[x]<sub[y])swap(x,y);
ata[y]=x;sub[x]+=sub[y];
umin(mn[x],mn[y]);
umax(mx[x],mx[y]);
}
//The key idea is there are at most 2*n^2 such pairs
void add(int x,int y){
assert(x+1<y);
//if rc=0, then rectangle on row (pos) in range (arr[pos][x],arr[pos][y]) is good
//if rc=1, then rectangle on column (pos) in range (arr[x][pos],arr[y][pos]) is good
if(!rc)row[x][y].pb(pos);
else col[x][y].pb(pos);
}
void solve(int x){
if(x>1 and vis[x-1]){
int a=mn[tap(x-1)]-1;
if(a>=1)add(a,x);
}
if(x<sz and vis[x+1]){
int b=mx[tap(x+1)]+1;
if(b<=sz)add(x,b);
}
}
void upd(int x){
vis[x]=1;
if(x>1 and vis[x-1])merge(x-1,x);
if(x<sz and vis[x+1])merge(x,x+1);
}
void f(){
for(int i=1;i<=sz;i++)
ata[i]=mn[i]=mx[i]=i,sub[i]=1,c[i]=i,vis[i]=0;
sort(c+1,c+sz+1,cmp);
for(int i=1;i<=sz;i++){
int j=i;
while(j<=sz and arr[c[j]]==arr[c[i]])solve(c[j++]);
for(int k=i;k<j;k++)upd(c[k]);
i=j-1;
}
}
void upd(int y,int x,int val){
for(;x<N;x+=x&(-x))F[y][x]+=val;
}
int get(int y,int x){
int res=0;
for(;x;x-=x&(-x))res+=F[y][x];
return res;
}
void relax(int rc,int x,int y){
if(!rc)
row[x][y].erase(unique(all(row[x][y])),row[x][y].end());
else
col[x][y].erase(unique(all(col[x][y])),col[x][y].end());
}
long long count_rectangles(std::vector<std::vector<int> > a) {
int n=int(a.size()),m=int(a[0].size());
if(n<3 or m<3)
return 0;
{
sz=m;
for(int j=1;j<=n;j++){
for(int i=1;i<=m;i++)
arr[i]=a[j-1][i-1];
rc=0;pos=j;f();
}sz=n;
for(int j=1;j<=m;j++){
for(int i=1;i<=n;i++)
arr[i]=a[i-1][j-1];
rc=1;pos=j;f();
}
}
int tmp,st=-1,en,cnt,who;
for(int i=1;i<=n;i++)
for(int j=i+2;j<=n;j++){
tmp=int(col[i][j].size());
relax(1,i,j);
for(int k=0;k<tmp;k++){
if(st==-1)st=col[i][j][k];
en=col[i][j][k];
if(k+1==tmp or col[i][j][k]+1!=col[i][j][k+1]){
for(int h=st;h<=en;h++)
addc[h].pb(mp(mp(i+1,j-1),en));
st=-1;
}
}
}
ll ans=0;
for(int i=2;i<m;i++){
tr(it,addc[i])upd(it->ff.ss,it->ff.ff,+1),remc[it->ss].pb(it->ff);
addc[i].clear();
for(int j=i;j<=m;j++){
if(j<m){
relax(0,i-1,j+1);
tmp=int(row[i-1][j+1].size());cnt=0;
for(int k=0;k<tmp;k++){who=row[i-1][j+1][k];
cnt++;ans+=get(who,who)-get(who,who-cnt);
if(k+1==tmp or who+1!=row[i-1][j+1][k+1])cnt=0;
}
}
tr(it,remc[j])upd(it->ss,it->ff,-1);
remc[j].clear();
}
}
return ans;
}
